title: The coalescent and the genealogical process in geographically structured population.
abstract: We shall extend Kingman's coalescent to the geographically structured population model with migration among colonies. It is described by a continuous-time Markov chain, which is proved to be a dual process of the diffusion process of stepping-stone model. We shall derive a system of equations for the spatial distribution of a common ancestor of sampled genes from colonies and the mean time to getting to one common ancestor. These equations are solved in three particular models; a two-population model, the island model and the one-dimensional stepping-stone model with symmetric nearest-neighbour migration.
authors.affiliation: Department of Biology, Faculty of Science, Kyushu University, Fukuoka, Japan.
authors.forename: M
authors.initials: M
authors.lastname: Notohara
mesh_terms: D005828:Genetics, Population; D005843:Geography; D008433:Mathematics; D008957:Models, Genetic; D011336:Probability